This paper presents two approaches to smoothing time trends in prevalence and estimating the underlying incidence of remissible infections. In the first approach, we use second order segmented polynomials to smooth a curve in a bounded domain. In the second, incidence is modeled instead and the prevalence is reconstructed using the recovery rate which is assumed to be known. In both approaches, the number of knots and their positions are estimated, resulting in non-linear regressions. Akaike Information Criterion is used for model selection. The method is illustrated with Syphilis and Gonorrhea prevalence smoothing and incidence trend estimation in Guinea-Bissau and South Africa, respectively.
Keywords: incidence rate; maximum likelihood estimation; model selection; prevalence; segmented polynomials.